关于级数的绝对收敛  

On absolutely convergent series

作　　者：杨云燕 

机构地区：[1]哈尔滨工业大学数学系,黑龙江哈尔滨150001

出　　处：《哈尔滨工业大学学报》2005年第8期1113-1115,共3页Journal of Harbin Institute of Technology

摘　　要：拓展了级数绝对收敛的概念.设(X,X′)是任意对偶系统,在X上找到了一个可容许拓扑τ,使得在(X,τ)上有界乘数收敛级数都是绝对收敛的,但是,当可容许拓扑τ′严格强于τ时,在(X,τ′)中,一定存在有界乘数收敛级数不是绝对收敛的.这个结果的建立主要借助于李容录的一致收敛引理[1]和Antosik-M ikus-insk i矩阵定理[2].The concept of absolute convergence is generalized. For every dual pair （X,X′）, There exists an admissible topology τ on X such that, in （X,τ）, bounded multiplier convergent series are absolutely convergent but in （X,τ′）, where the admissible topology τ′ is strictly stronger than τ, there exist bounded multiplier convergent series which are not absolutely convergent. This result is based on the Uniform Convergence Lemma of LI Rong-lu and Antosik-Mikusinski Basic Matrix Theorem.

关 键 词：绝对收敛 有界乘数收敛 等度连续 可容许拓扑 Antosik-Mikusinski矩阵定理 

分 类 号：O173[理学—数学]